DOF question 35mm vs. 4x5

[Nathan Potter]

Dan, I had forgotten about that Kodak publication N12-B and just found it in a storage box. Mine is just N12 and includes A and B. It is old, 1977, and I suspect may come up occasionally on Ebay. Worth getting, but the closeup technology has changed greatly since then, where now focus scanning is state of the art for DSLR work.

Returning to the OP queries I can say what I do about DOF estimation when I want to set a far limit of resolution at infinity and want to know where the near limit is.
Using standard formula for determining the near limit and far limit I just generate a pocket chart for each lens I use which indicates the hyperfocal distance, the near limit, far limit set at ∞ and for a COC of 20µm and 40 µm. Then, often without shifts or tilts, I'll estimate the hyperfocal distance and get that in focus on the GG and go from there. Recently I use a rangefinder; when I remember it. Deriving my charts assume no magnification factors. The near and far limits are computed by simple algebra thusly:

Df =µf^2/(f^2-NCµ) for the far limit and Dn-µf^2/(f^2+NCµ) for the near limit.

Df = far limit
Dn = near limit
µ = object conjugate distance
f =lens focal length
N = f/no.
C = circle of confusion

If I ignore a near and far limit and just want a depth of field then DOF = 2µ^2NC/f^2.

To determine the hyperfocal distance which assumes the far limit at ∞ I use: H = f^2/NC + f where H = hyperfocal distance.

So a recently done pocket chart for the Schneider 47 mm XL is shown below.

f/no. H in ft. RANGE (ft) H in ft. RANGE (ft)
(COC = 20 µm) (COC = 40 µm)
5.6 165 82 to ∞ 82 41 to ∞
8 45 22 to ∞ 22 11 to ∞
11 33 16 to ∞ 16 8 to ∞
16 22 11 to ∞ 11 5 to ∞
22 16 8 to ∞ 8 4 to ∞
32 11 5 to ∞ 5 3 to ∞
45 8 4 to ∞ 4 2 to ∞
64 5.5 2.7 to ∞ 2.7 1.4 to ∞

A really handy field chart for a couple of common Circles of Confusions for critical work with the caveat of finding the hyperfocal distance with some degree of accuracy. Note that the 47 XL approaches a pinhole for DOF but the optics provides much better resolution when needed.

Nate Potter, Austin TX.

[Nathan Potter]

Well crap and sorry, the Forum software doesn't preserve the spacing for charts; but maybe one can figure it out. If there is some interest I can post some actual charts.

Nate Potter, Austin TX.

[Dan Fromm]

Dan, I had forgotten about that Kodak publication N12-B and just found it in a storage box. Mine is just N12 and includes A and B. It is old, 1977, and I suspect may come up occasionally on Ebay. Worth getting, but the closeup technology has changed greatly since then, where now focus scanning is state of the art for DSLR work.

Yes it has, hasn't it? The ideas are still good, though, and transfer from small format (Instamatics!) for which the Closeup pamphlet was written, to larger formats.

Unfortunately the scanning approach fails completely for the subjects that got me into closeup photography. Unconstrained fish in aquaria. Kinda like SEM work. Infinite DoF and high resolution but the subject has to be safely dead.

Funny thing is, the only time I worry about DoF when I'm shooting out and about is when I want to isolate the subject from the background. This involves shooting at a relatively large aperture at which viewing on the GG is easy. Interestingly, with some of my faster lenses I can see the trade-off between isolating the subject and pleasing rendition of the background. I sometimes have to give up a little of one to get more of the other. I'm not sure that calculations would help much there.

Cheers,

Dan

[Nathan Potter]

Motion is not friendly to closeup work. That would be pure frustration for me.

By the way, in my post above I picked 20 and 40 µm as a COC and forgot to mention that a diffraction limit cuts that to a larger value at the point in f/stop where the COC approximately equals the diffraction limit.

So, for example, with the 47 XL at f/22 the COC is about 20 µm; at f/32 the COC is about 30µm and at f/45 the COC is about 40 um and so on. This from the diameter of an Airy disk which is D = 2.44 X lamda X N, or roughly 1.22 N at .5 µm.

In fact about the only time I worry about DOF is for landscape work where I want the near and far in fine focus.

Nate Potter, Austin TX.

[Leonard Evens]

Jeff Conrad's discussion does a good job of explaining what is going on, and anyone who really want to understand the subject should read his article.

But I'm firmly of the belief that there is no way to really understand the subject without going through the mathematics, amply described in Jeff's article.

I notice that no one made any effort to go into the mathematics, and, perhaps, that is the wisest course, but I will take a chance and do so.

DOF is a mathematical concept in geometric optics, and if you are willing to make the effort, a lot that seems mysterious becomes clear. Let me illustrate my point with the formula for hyperfocal distance.

H = f + f^2/(Nc)

where f is the focal length of the lens, N is the f-number used, and c is the diameter of the largest acceptable circle of confusion. (Since usually f is much smaller than f^2/(Nc), one can usually get by with the approximation

H ~ f^2/(Nc)
)

If you know the hyperfocal distance, you can calculate everything you may want to know about depth of field.

The quantity c is what is missing from most of the previous responses. It is a measure of how sharp you need the image to be in the negative in the camera. Unless one is making contact prints, one is more interested in what the viewer of the final print sees, and the final print will be enlarged from the image in the camera. Thus, typically, to make an 8 x 10 print, a 35 mm negative must be enlarged about eight times, while a 4 x 5 negative must be enlarged twice. That means you need to use a value of c about one fourth as large for a 35 mm negative as for a 4 x 5 negative. That in turn means that if the focal length f and f-number N are the same, you will get a hyperfocal distance about four times larger for the same size final print with a 35 mm format image than with a 4 x 5 format image.

When you focus at the hyperfocal distance, everything (in the final print) between half the hyperfocal distance and infinity will be in focus. So, in that case, the larger the hyperfocal distance the less the depth of field, which means that for the same focal length lens and the same f-number, you will have significantly less depth of field (in the final print) with 35 mm format than with 4 x 5 format.

If you look at the formulas which apply when focused at any other specific distance, you see that the same is true. With the same focal length and the same relative aperture, you have significantly less depth of field if the original format is 35 mm than if it is 4 x 5.

But you have to be careful about generalizing this. Similar calculations show that if you change the focal length so that the angle of view is the same in the two cases, e.g., so the 35 mm format focal length is about one fourth of the 4 x 5 format focal length, then the depth of field (in the final print) is significantly greater if the original image is in 35 mm format than if the original image is in 4 x 5 format.

This is no a contradiction, if you keep in mind that while, for example, 100 mm is a relatively long lens for 35 mm format, it is relatively short lens for 4 x 5 format. Of course if the format stays the same, longer lenses have less depth of field than shorter lenses, but to see how this plays out when you change formats, you need to look at the mathematics.

(In particular, if in the formula f^2/(Nc) you multiply c by 4 but keep f the same, you divide the total fraction by 4. But if you multiply c by a factor of 4 and at the same time multiply f by the same factor, because f^2 appears in the numerator, the total effect is to multiply f^2/(Nc) by 4. In other words, just multiplying c by 4 has the opposite effect to multiplying c by 4 and at the same time multiplying f by 4.)

Note that there is no way to understand how these different factors play out in specific situations without doing the mathematics. A purely verbal description can't do it.

[Leigh]

earlier Hasselblad lenses have shutter duration coupled to f-stops - a feature I dislike but live with.

Modern (Prontor shutter) Hasselblad lenses still have the shutter/aperture coupling.

The difference is with the Compur shutters, it was engaged by default and you had to press a lever to decouple the two.

With the Prontor shutters, that feature is disengaged by default, and you must press a lever to couple them.

- Leigh

[Tin Can]

Perhaps a few images could help. Some of us, like me, need all the help visually we can find. Of course there are infinite variation, but portrait, interior and something distant could illustrate this in 6 images. Use extremes for examples.

Thanks for everything so far!

btw, I have forgotten how to solve H ~ f^2/(Nc) that little '^' eludes my memory!

Jeff Conrad's discussion does a good job of explaining what is going on, and anyone who really want to understand the subject should read his article.

But I'm firmly of the belief that there is no way to really understand the subject without going through the mathematics, amply described in Jeff's article.

I notice that no one made any effort to go into the mathematics, and, perhaps, that is the wisest course, but I will take a chance and do so.

DOF is a mathematical concept in geometric optics, and if you are willing to make the effort, a lot that seems mysterious becomes clear. Let me illustrate my point with the formula for hyperfocal distance.

H = f + f^2/(Nc)

where f is the focal length of the lens, N is the f-number used, and c is the diameter of the largest acceptable circle of confusion. (Since usually f is much smaller than f^2/(Nc), one can usually get by with the approximation

H ~ f^2/(Nc)
)

If you know the hyperfocal distance, you can calculate everything you may want to know about depth of field.

The quantity c is what is missing from most of the previous responses. It is a measure of how sharp you need the image to be in the negative in the camera. Unless one is making contact prints, one is more interested in what the viewer of the final print sees, and the final print will be enlarged from the image in the camera. Thus, typically, to make an 8 x 10 print, a 35 mm negative must be enlarged about eight times, while a 4 x 5 negative must be enlarged twice. That means you need to use a value of c about one fourth as large for a 35 mm negative as for a 4 x 5 negative. That in turn means that if the focal length f and f-number N are the same, you will get a hyperfocal distance about four times larger for the same size final print with a 35 mm format image than with a 4 x 5 format image.

When you focus at the hyperfocal distance, everything (in the final print) between half the hyperfocal distance and infinity will be in focus. So, in that case, the larger the hyperfocal distance the less the depth of field, which means that for the same focal length lens and the same f-number, you will have significantly less depth of field (in the final print) with 35 mm format than with 4 x 5 format.

If you look at the formulas which apply when focused at any other specific distance, you see that the same is true. With the same focal length and the same relative aperture, you have significantly less depth of field if the original format is 35 mm than if it is 4 x 5.

But you have to be careful about generalizing this. Similar calculations show that if you change the focal length so that the angle of view is the same in the two cases, e.g., so the 35 mm format focal length is about one fourth of the 4 x 5 format focal length, then the depth of field (in the final print) is significantly greater if the original image is in 35 mm format than if the original image is in 4 x 5 format.

This is no a contradiction, if you keep in mind that while, for example, 100 mm is a relatively long lens for 35 mm format, it is relatively short lens for 4 x 5 format. Of course if the format stays the same, longer lenses have less depth of field than shorter lenses, but to see how this plays out when you change formats, you need to look at the mathematics.

(In particular, if in the formula f^2/(Nc) you multiply c by 4 but keep f the same, you divide the total fraction by 4. But if you multiply c by a factor of 4 and at the same time multiply f by the same factor, because f^2 appears in the numerator, the total effect is to multiply f^2/(Nc) by 4. In other words, just multiplying c by 4 has the opposite effect to multiplying c by 4 and at the same time multiplying f by 4.)

Note that there is no way to understand how these different factors play out in specific situations without doing the mathematics. A purely verbal description can't do it.

[Jeff Conrad]

Take a look at H. Lou Gibson's little pamphlet Photomacrography (Kodak Publication N12-B, incorporated in Kodak Publication N-16 Closeup Photography and Photomacrography). He does the calculations and shows example photographs in which the zone of acceptable sharpness shrinks on stopping down. There are limits to what can be done.

Paul Hansma did a similar analysis in the March/April 1996 issue of Photo Techniques “View Camera Focusing in Practice.” Unlike Gibson, Hansma assumed infinity focus, so he didn’t deal with the significant degradation that you get in closeup work. Hansma’s article is available on the site under References in Q.T. Luong’s article How to select the f-stop. Despite what I say in my paper, the article is four GIFs rather than PDF.

Gibson and Hansma both assumed that combined defocus and diffraction could be modeled by a root-square combination of defocus and diffraction blur spots. Gibson promised a more complete description of the basis for this but I’m not sure the article was ever written. As I understand it, the root-square (or sometimes linear) combination of resolutions is more a rule of thumb than hard science; however, the results—especially Hansma’s—are quite similar to what I got using calculated MTFs. This would seem to suggest that we’re at least in the ballpark, and that as Dan said, there sometimes are limits to what can be done—especially with closeups.

It’s a very interesting article; Gibson attempts to address some additional causes of image degradation that Hansma and I ignore.

[Dan Fromm]

Motion is not friendly to closeup work. That would be pure frustration for me..

It is at times for me too. I shot fish with KM using a 35 mm SLR, proper macro lens, and flash illumination. All I had to do was get the fish to perform front and center and track them by teetering. The flash stopped motion, both subject and camera.

And then I started shooting flowers with the same gear. Much easier than fish, until I went up in format. Wind kills me. Flash stops motion, but the intended plane of best focus can move between the time I've focused and composed and the time the shutter has been closed and cocked, film holder inserted, dark slide pulled, ...

Jeff, in photography ball park is often close enough. But you know that too.

I've done my calculations, when I bother, to see what's clearly impossible and, as I've mentioned, to design closeup flash rigs. That's an interesting problem that people with auto-everything cameras tend to ignore, but it has some significance for those of us who still use auto-nothing cameras. Following up on a hint in a discussion of Spiratone's MacroDapter in, IIRC, MP, I've designed a number of flash rigs that give good exposure with fixed power flashes and a fixed aperture setting (nominal, not effective) over a useful range of magnifications. If you're interested I can give you a link to the spreadsheet. The current realization of the design incorporates a Jones of Hollywood flash bracked that's similar to the MacroDapter but that offers better geometry. The flash design spreadsheet reports, among other things, the largest enlargement possible given the diffraction limit at the effective aperture. Its just one discouragement after another.

Cheers,

Dan

[ic-racer]

Is is correct that LF lenses and 35mm lense of the same focal length and set to the same f/stop would produce images with different DOF's??? If possible can someone give an "Explanation for Dummies" type answer as to what the difference and why?

The circles of confusion will be the same size, but DOF calculation involves other variables, like viewing distance.